Problem: Convert $\dfrac{13}{3}$ to a mixed number.
First, divide the numerator by the denominator. $13 \div 3 = {4}\ \text{ R } {1}$ So the improper fraction has $4$ wholes in it, which is equal to ${4} \times \dfrac{3}{3} = {\dfrac{12}{3}}$ This quotient $4$ is the whole number part of the mixed number. We also have a remainder of $1$ , though. That represents the $\dfrac{{1}}{3}$ remaining from the improper fraction; it wasn't enough to be another whole number. The converted mixed fraction is ${4}\ {\dfrac{1}{3}}.$ Note that if we add up the two pieces of our mixed fraction, ${\dfrac{12}{3}} + {\dfrac{1}{3}}$, we get the original improper fraction $\dfrac{13}{3}$.